This research will study development of functional understanding of probability and expected value from age 4 to 12 years. This involves understanding of probability and value concepts as they act together, which is typical of everyday life. Key features of method are the use of continuous, quantitative judgments, together with tasks that involve information integration. This allows direct diagnosis of functional understanding in terms of response pattern. Thus, a pattern of parallelism is the sign of an addition rule and a linear fan pattern is the sign of a multiplication rule. This method of rule diagnosis is practicable with individual children as young as 4 years of age. The proposed experiments begin with a very simple task of probability judgment that is expected to demonstrate fairly advanced functional understanding of probability as early as 5-6 years of age. Subsequent experiments extend this same task in two ways: to include more general concepts of expected value and to involve greater processing demands on attention and memory. Concepts of probability and expected value are frequent in everyday life. In health psychology, for example, medical personnel diagnose and prescribe on the basis of uncertain information, and patients decide whether to seek and to follow prescribed treatments on the basis of their everyday notions about probability and value. These health decisions are well-known to suffer numerous biases, but little is known about developmental origins of these biases. By looking to developmental origins of cognitive processes of probability and value together, this research aims to contribute to theoretical and practical understanding of decisions of everyday life.